This invention relates to investigation of subsurface formations surrounding a borehole, and, more particularly, to a borehole logging method and apparatus for determining the porosity and/or formation factor of subsurface formations.
It is generally accepted that the resistivity of a "clean" formation (i.e., one relatively free of clay) is proportional to the resistivity of the fluid with which it is saturated. The constant of proportionality, F, is called the "formation factor" (or, sometimes, the "formation resistivity factor"). Therefore, if a clean formation sample of resistivity R.sub.o is fully saturated with fluid of resistivity R.sub.w, we have ##EQU1## If formation resistivity is measured and F is known, the fluid resistivity can be obtained from relationship (1).
The porosity, .phi., of a formation is the fraction of the total volume occupied by pores or voids. Formation factor is a function of porosity, and also a function of pore structure and pore size distribution. One accepted relationship between porosity and formation factor is ##EQU2## where a and m can both vary for different types of formations. In a compacted formation, the values sometimes used are a=1 and m=2, that is: ##EQU3##
There are various relatively reliable well logging techniques for determining the porosity of formations, although additional or alternate source information concerning porosity is always desirable. Regarding determination of formation factor, a certain amount of guesswork is usually involved. Therefore, any inputs which lead to a more accurate value of formation factor are particularly valuable in improving the results of electrical logging.
With regard to sonic logging, it is advantageous to study properties of sonic propagation in various media. It is generally recognized that an important aspect of acoustic attenuation and dispersion in porous fluid-saturated media is due to the relative motion that can occur between the solid and fluid parts thereof. A theory which studies the displacements of the two components was developed in the prior art, and it was proposed that a sonic wave propagation model for fluid-saturated porous media should include, in addition to the expected compressional and shear waves (which are used in conventional sonic logging), a wave called a second bulk or "slow compressional wave" propagating at a velocity which is slower than that of the compressional and shear waves. [See M. A. Biot, "Theory of Propagation of Elastic Waves in a Fluid-Saturated Porous Solid", Journal of Acoustical Society of America, Vol. 28, pages 168-191 (1956)]. The slow compressional wave was recently described for use in well logging. In particular, the copending U.S. patent application Ser. No. 174,396 of T. Plona, now abandoned assigned to the same assignee as the present invention, discloses techniques for applying sonic energy to formations to cause propagation therein of a slow compressional wave, detecting and measuring properties of the slow compressional wave propagating in the formations, and determining the permeability of the formations from the measured properties.
It is an object of the present invention to utilize certain measurements of the slow compressional wave in determining properties of porosity and/or formation factor of formations through which the slow compressional wave has propagated.